Chaos

Manipulate the slider to witness the changes in the system
Change the parameter (slider a) and answer the following questions. Refer to the time series (blue window) to answer the questions.
1. Set the slider equal to 1. How does the system behave?
2. Set the slider to a negative value. How does the system behave?
3. Set the slider to some positive value other than 1. How does the system behave?
4. For what values of "a" is the system chaotic?
5. For what parameter will the sequence converge?
6. Can we predict the behavior of this system? Why or why not?